Exam (elaborations) Class 10 boards

CLASS – X
SUBJECT- BASICMATHEMATICS (241)
SAMPLE QUESTION PAPER (2023-24)
TIME ALLOWED: 3 HRS MAXIMUM MARKS: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 sourced based/Case Based/passage based/integrated units of
assessment (4 marks each) with sub-parts of the values of 1, 1 and 2 marks each
respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs
of 3 marks and 2 Questions of 5 marks has been provided. An internal choice has
been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take π =22/7 wherever required if not
stated.

SECTION A

1. If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime
numbers, then HCF (a,b) is:
a) xy b) xy2 c) x3y3 d) x2y2
2. The LCM of smallest two-digit composite number and smallest composite number is:
a) 12 b) 4 c) 20 d) 44
3. If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of
k is
1 1
a) -2 b) c) 3 d) 2
2

4. The pair of equations y = 0 and y = -7 has:
a) One solution b) Two solutions c) Infinitely many solutions d) No solution
5. Value(s) of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is :
a) 0 only b) 4 c) 8 only d) 0,8
6. The distance of the point(3,5) from x-axis(in units) is:
a) 3 b) - 3 c) 5 d) -5
𝐴𝐵 𝐵𝐶 𝐶𝐴
7. If in ∆ ABC and ∆ PQR, we have 𝑄𝑅 = 𝑃𝑅 = 𝑃𝑄 then:

a) ∆PQR ~∆CAB b) ∆PQR ~∆ABC c) ∆CBA ~∆PQR d) ∆BCA ~∆PQR

1

, 8. Which of the following is NOT a similarity criterion?
a) AA b) SAS c) AAA d) RHS
9. In figure, if TP and TQ are the two tangents to a circle
with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60° (b) 70° (c) 80° (d) 90°
4
10. If cos A = then the value of tan A is:
5
3 3 4 1
a) b) c) d)
5 4 3 8

11. If the height of the tower is equal to the length of its shadow, then the angle of
elevation of the sun is _____
a) 30° b) 45° c) 60° d) 90°
12. 1 – cos2 A is equal to
a) sin2 A b) tan2A c) 1 – sin2A d) sec2A
13. The radius of a circle is same as the side of a square. Their perimeters are in the ratio
a) 1:1 b) 2:𝜋 c) 𝜋 : 2 d) √𝜋 : 2
14. The area of the circle is 154cm2. The radius of the circle is
a) 7cm b) 14cm c) 3.5cm d) 17.5cm
15. When a die is thrown, the probability of getting an even number less than 4 is
a) 1/4 b) 0 c) 1/2 d) 1/6
16. For the following distribution:
Class 0-5 5-10 10-15 15-20 20-25
10 15 12 20 9
Frequency

The lower limit of modal class is:
a) 15 b) 25 c) 30 d) 35
17. A rectangular sheet of paper 40cm x 22cm, is rolled to form a hollow cylinder of
height 40cm. The radius of the cylinder(in cm) is :
80
a) 3.5 b) 7 c) d) 5
7

18. Consider the following frequency distribution:
Class 0-6 6-12 12-18 18-24 24-30
12 10 15 8 11
Frequency

2